Prove that the area of an equilateral triangle described on one side of the square is equal

Prove that the area of an equilateral triangle described on one side of the square is equal to half the area of the equilateral triangle described on one of its diagonal.

Answer

Let the side of the square be a units

AC² = a² + a² = 2a²

AC = $ \sqrt{2} a $ units

• Exam Year: 2018